Abstract
A simple two-dimensional shear deformable finite beam element is developed in order to examine the effect of the high order interpolation on the modes of deformation of the beam cross section using the ANCF finite element. The new element allows for effect of warping that cannot be captured using previously introduced ANCF beam elements, and relaxes the assumption of planar cross section. The displacement field of the new element is assumed to be cubic in the axial direction and quadratic in the transverse direction. Using this displacement field, new shape functions are formulated and include the quadratic of the transverse direction instead of the linear expression. The displacement gradient and transverse strain component obtained using the new higher order element are introduced. Numerical example is presented in order to compare the results obtained using the new finite element and the results obtained using previously developed ANCF finite element. The results reveal that the cross section remains as a curve surface not a planar one.
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